4 ms·

I'm sorry, the puzzle is asking for a global property. The new text has the adjustments.

• sharpneli 16y ago
  I think I got it now. Don't read this if you are afraid of possible spoiling. We are looking for a graph with highest possible minimum vertice count for any single node. The answer is 6. This graph comes from simply making a hexagonal tiling with node on center and vertices going trough edges. Any tiling with more angles does not produce a planar graph and we'd have to insert polygons with less vertices and thus less neighbours and therefore lowering the smallest edge count.
  • lisper 16y ago
    I don't think it's possible to tile a sphere with hexagons. You have to throw a couple of pentagons in. http://en.wikipedia.org/wiki/Geodesic_dome http://en.wikipedia.org/wiki/Geodesic_dome
    • sharpneli 16y ago
      True. So for a spherical topology the largest minimum is 5. However for toroidal topology the largest minimum is 6.